question stringlengths 16 86 | problem stringclasses 8
values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve: |2x + -8| ≤ 16 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 12 |
Solve: |5x + 11| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 0 |
Solve for x: -6(x + 6) = -48 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 2 |
Solve for x: -1(x + -10) = 15 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
What is 123% of 700? | Compute the percent value (integer-safe). | Compute 123/100 × 700. | 861 |
Solve: |3x + -12| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: 0x + 8x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 8x - 5y |
Solve for x: 4(x + -2) = 0 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 2 |
Solve: |-6x + 5| = 19 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 4 |
Solve for x: -8(x + 11) = -112 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 3 |
Solve: 10x + 17 < -123 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -14 |
Simplify: -7x + -1x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -8x + 1y |
Solve: |8x + 18| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -2 |
If each item costs 8 dollars and the total cost is 208, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 26 |
What is -36% of 25? | Compute the percent value (integer-safe). | Compute -36/100 × 25. | -9 |
What is 77% of 200? | Compute the percent value (integer-safe). | Compute 77/100 × 200. | 154 |
What is 28% of 50? | Compute the percent value (integer-safe). | Compute 28/100 × 50. | 14 |
If each item costs 19 dollars and the total cost is 209, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 11 |
If each item costs 10 dollars and the total cost is 0, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 0 |
What is 79% of 0? | Compute the percent value (integer-safe). | Compute 79/100 × 0. | 0 |
Simplify: -2x + -7x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -9x - 5y |
Solve: |8x + -6| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: -8x + -6x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -14x - 4y |
Simplify: 2x + 0x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x - 3y |
Solve: |-8x + -12| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -1 |
Solve: |-6x + -14| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: 10x + -10 ≥ 90 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 10 |
If each item costs -2 dollars and the total cost is 10, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -5 |
Solve for x: 8(x + 14) = 112 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 0 |
If each item costs -8 dollars and the total cost is 144, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -18 |
If each item costs 20 dollars and the total cost is -140, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -7 |
Solve: |5x + 3| = 20 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: -11x + -7 = -227 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 20 |
Solve for x: -2(x + 13) = -52 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 13 |
If each item costs 19 dollars and the total cost is -19, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -1 |
Solve: |-5x + -1| = 20 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: 5x + -10 < -105 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -19 |
Simplify: 6x + 6x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 12x - 7y |
Solve: -9x + 5 > 5 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 0 |
Solve: -10x + 18 < -82 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 10 |
Solve for x: -7(x + 9) = -28 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
What is 66% of 350? | Compute the percent value (integer-safe). | Compute 66/100 × 350. | 231 |
Solve: |6x + 8| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -1 |
Solve: -5x + -20 < 10 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -6 |
Solve: |4x + -5| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 5 |
Solve: |2x + -12| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 6 |
Solve: |5x + 10| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: -4x + 3x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x - 3y |
Solve: -6x + -14 ≥ -56 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 7 |
What is 26% of 200? | Compute the percent value (integer-safe). | Compute 26/100 × 200. | 52 |
Solve: |7x + 9| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ -1 |
Solve for x: -1(x + 5) = -17 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 12 |
Solve for x: 5(x + -6) = -105 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
Solve: |7x + -6| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs 20 dollars and the total cost is -40, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -2 |
If each item costs 10 dollars and the total cost is -170, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -17 |
Solve for x: 5(x + -14) = -90 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -4 |
Solve for x: 4(x + -11) = -76 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -8 |
Solve for x: 4x + 24 = -4 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -7 |
Solve for x: -5(x + 0) = 5 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -1 |
Solve: |-6x + -8| ≤ 15 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 1 |
What is 7% of 500? | Compute the percent value (integer-safe). | Compute 7/100 × 500. | 35 |
Solve for x: 1x + 8 = 7 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -1 |
What is 109% of 900? | Compute the percent value (integer-safe). | Compute 109/100 × 900. | 981 |
Solve for x: -3x + -27 = -15 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -4 |
If each item costs -3 dollars and the total cost is 0, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 0 |
Solve for x: 4x + 8 = -8 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -4 |
Solve: -3x + -9 ≤ 21 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -10 |
Solve: -7x + -17 > -157 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 20 |
If each item costs 12 dollars and the total cost is 36, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 3 |
Solve for x: 2(x + -3) = 12 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 9 |
If each item costs 15 dollars and the total cost is -105, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -7 |
Solve: |6x + 7| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 1(x + 13) = 6 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -7 |
What is 43% of 400? | Compute the percent value (integer-safe). | Compute 43/100 × 400. | 172 |
What is 53% of 1000? | Compute the percent value (integer-safe). | Compute 53/100 × 1000. | 530 |
What is -30% of 30? | Compute the percent value (integer-safe). | Compute -30/100 × 30. | -9 |
Solve for x: -5x + 3 = -72 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 15 |
Simplify: -4x + 6x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x + 2y |
Solve for x: 4(x + 6) = -8 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -8 |
Simplify: 3x + 4x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7x - 5y |
If each item costs 18 dollars and the total cost is 216, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 12 |
What is 9% of 900? | Compute the percent value (integer-safe). | Compute 9/100 × 900. | 81 |
Solve: |8x + 11| ≤ 0 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
If each item costs -6 dollars and the total cost is -18, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 3 |
Simplify: 4x + 0x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x - 4y |
What is 85% of 140? | Compute the percent value (integer-safe). | Compute 85/100 × 140. | 119 |
If each item costs -4 dollars and the total cost is -44, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 11 |
Solve for x: -10x + 9 = -111 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 12 |
Solve: -4x + -15 ≤ -27 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 3 |
Solve: |7x + 0| = 6 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-6x + 13| ≤ 8 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 3 |
Solve: |-7x + -7| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 0 |
Solve: 6x + 14 < 86 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 12 |
Solve: |7x + -1| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-1x + -6| ≤ 18 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -24 ≤ x ≤ 12 |
Solve: |-4x + 15| = 11 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 1 |
Solve: |8x + 9| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs -9 dollars and the total cost is -117, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 13 |
Solve: |-8x + -14| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
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